Sampling The Olympics

# 4. Does Hosting Help?

Suggested Learning Intentions

• To synthesise and analyse data from a variety of sources to make inferences
• To informally identify outliers and explain their impact

Sample Success Criteria

• I can use data that includes outliers to make inferences about a population
• I can identify outliers and explain their impact on a data set
• I can explain my thinking and solutions using a range of manipulatives
• Student access to the internet will be required for them to complete their own research
• Computer, laptop or tablet access

Does Hosting Help? is an investigation into the impact that hosting the Olympic Games has on the performance of the host nation at the Games.

Alternatively, your students may like to use the approach outlined in this stage to investigate the home ground advantage of their own favourite sporting team. Statistics are freely available online regarding the performance of Australian and international sporting teams. Students can still be exposed to relevant and valuable mathematical content, but in a context that is potentially more meaningful for them.

Facilitate a class discussion about the sporting term ‘home ground advantage’. Invite students to contribute their own experiences of home ground advantage.

You may like to draw upon ideas presented in this article as part of the discussion, or provide excerpts from the article for students to read and discuss.

Pose the following research questions for students to consider:

Is ‘home ground advantage’ a concept that applies to the Olympics?

How does hosting the Olympic Games impact the performance of the host nation?

1. Discuss ways in which the performance of a nation at the Olympic Games could be measured

Invite students to discuss how they could investigate the impact that hosting the Olympic Games has on the performance of the host nation.

Guide students towards the understanding that there are different ways of measuring the performance of a nation at any one Olympic Games. Primarily, these are:

• the number of gold medals won by the nation
• the total number of medals won by the nation
• the overall ranking of the nation in the medal tally.

Explain that students will be investigating the performance of several host countries.

Refocus students on the research question – “How does hosting the Olympic Games affect the performance of the host nation” and discuss with students how they could undertake research so that they can respond to this question. Guide students towards the understanding that measuring the performance of a nation over several successive Olympic Games, including a hosted Games, may allow us to identify the impact of hosting on their performance.

Ask students to select at least one measure of performance as the focus of their research. For example, one student may choose to investigate both the overall ranking and the number of gold medals won by the host nation, while another student may choose to investigate only the total medals won by the host nation.

2. Compile the population data and select a sample from the population

Provide an opportunity for students to research the nations that have hosted the Olympic Games. Use their research to collaboratively compile a list of nations who have hosted the Games and explain that this list constitutes the population from which samples will be drawn. Include countries who have hosted the Winter Olympics in this research to broaden your population if desired.

Ask students to select a sample of nations to analyse, using a recognised sampling technique. Provide students autonomy with regards to the sample size they select.

3. Research the performance of the sampled nations

Once students have selected their sample of nations and their measure of performance, provide time for them to collect the data related to the performance of their sampled nations over the time period they wish to investigate. For example, one student may choose to research the performance of a host nation at three successive Olympic Games (with the second of the three being the hosted Games) while other students may research the performance at five successive Olympic games (with the third of the five being the hosted Games).

Students present their data in a table or graph.

Enable students by co-constructing or modelling the research for one particular host nation with students, and analysing the data together as a group.

The table and graph below provide an example of how the research could be presented and modelled for students. This example relates to the 1956 Summer Olympic Games, held in Melbourne. Australia’s performance at five successive Olympic Games has been researched.

After co-constructing these tables and graphs with students, invite students to share what they notice from the tables and graphs with you, using these prompts, if required:

• What do you notice about the information in the table and graphs?
• Why do you think the years 1948, 1952, 1956, 1960 and 1964 were investigated?
• How do these help us answer the question about how hosting the Olympic Games affects the performance of the host nation?
• Do you think we would notice similar things for other host nations? How could you check?

Once students have understood how the research for one nation can be conducted and presented, they may have the confidence to replicate this process for other host nations.

Refer to Creating tables from the Literacy in Mathematics section of the Literacy Teaching Toolkit, to support you to scaffold students to understand how tables can be used to represent and compare information.

4. Use the collected data to introduce the concept of outliers

Invite students to share preliminary observations from their research (tables and graphs). Students may comment on the fact that nations have consistently performed ‘better’ in Olympic Games that they have hosted, when compared to Games held in other countries. Establish, through discussion, a shared understanding amongst students that hosting the Olympic Games is generally associated with improved performance.

Ask students to use their selected measure/s of performance to quantify the performance of some of their sampled nations, both with and without the host year included.

For example, a student may have chosen the number of gold medals won as their measure of performance. For the 1956 Olympics, the student could determine the average number of gold medals won during the research period (1948 – 1964). With the host year included, Australia won a mean of 7 gold medals per Games during this period. With the host year excluded, Australia won a mean of 5.5 gold medals per Games.

Discuss the differences in these results and ask students to consider why they may be different. Students may begin to demonstrate an intuitive understanding of outliers in the language they use.

Provide students with a definition for the term outlier and discuss other data sets where outliers may naturally occur.

5. Investigate and apply different mathematical techniques to quantify the impact of hosting the Games

Discuss with students how they might refine their preliminary observations to understand the impact of hosting the Olympic Games on the performance of the host nation better. Explain that investigating the change in their collected data more deeply, they may able to better quantify the impact of hosting the Olympic Games.

There are several ways in which this could be done. Some measures include:

• The average (mean or median) percentage increase in the medal tally from the Games prior to hosting to the host Games, across the sample nations.
• The difference between the average medal tally from Games held either side of the hosting year, and the medal tally at the host Games, in either absolute or percentage terms.
• The average improvement in ranking position between Games that are not hosted and Games that are hosted.

Ask students to select at least one way of quantifying the effect of hosting the Olympic Games on the performance of the host nation. Guide students to construct statements that communicate their findings simply and eloquently. Sample statements may include:

• On average, host nations win 25% more gold medals when they host the Olympic Games, compared to the number of gold medals they win at the Games just before and just after.
• On average, host nations improve their ranking by 4 places when they host the Olympic Games, compared to their average performance in the two Olympic games held prior.

Provide opportunities for students to share and justify their statements to one another and to the class.

Areas for Further Exploration

1. Using the data to predict future performance

Once students have constructed their own statements, invite them to use their statements to predict, with justification, the performance of a host nation at an upcoming Olympic Games.

For example, a student may have stated that the total number of medals won by the host nation is typically 30% higher than their total medal tally at the previous two games. Students could use this statement to predict the number of medals that will be won by the host nation at the next Olympics.

These predictions could be shared, submitted, or stored in a class time capsule, to be opened after the Games.

This stage introduces the concept of outliers, and the effect they can have on summary statistics. It also provides opportunities for students to use percentages to explain the change in a value. Consider the progress made by students when determining which skills and concepts you select to review.

One suggested concept for review is presented below.

1. Outliers are values that are markedly different from the rest of a set of a data, and can impact on statistics used to represent the data

You may wish to emphasise the following concepts:

• Outliers can be visually identified from either a data table or a graphical representation of the data.
• Outliers can be a result of errors made when recording a set of data (for example, such as writing down 15 instead of 155 to represent someone’s height).
• Outliers can also reflect the natural variation in some sets of data (for example, temperature data).
• Outliers may have an impact on some summary statistics (e.g., mean and range) used to represent a set of data, but may not have an impact on other statistics (e.g. median and mode).
• We may choose to exclude outliers when calculating summary statistics or choose to use certain summary statistics over others when working with data that includes outliers.

You could support students to consolidate their understanding of outliers by providing further opportunities to work with data sets involving outliers. These may include:

• climate data during periods of extreme temperature, rainfall, or drought
• data related to house prices in a particular suburb or town.

Ask students to calculate different summary statistics for these sets of data, both including and excluding the outlier. Discuss the impact that the outlier has on the statistics, and whether, for example, the mean, median or mode would be a more appropriate way of representing data sets that contain outliers.

State Government of Victoria (Department of Education and Training), 2019. Creating Tables. [Online]
Available at: www.education.vic.gov.au/school/teachers/teachingresources/discipline/english/literacy/pages/lim_creatingtables.aspx
[Accessed 15 March 2022].

Thomas, A., 2003. Fighting the Home Advantage, ABC. [Online]
Available at: https://www.abc.net.au/science/articles/2003/06/19/2858666.htm
[Accessed 15 March 2022].